To take into account the inter-sentence dependencies and the discourse structure of documents, many extractive summarizers [1]}, [2]} use the well-known LexRank algorithm [3]} to compute sentence importance based on the concept of eigenvector centrality in a graph representation of sentences.
LexRank builds for \(\mathcal {D}\)  a graph \(\mathcal {G}=(\mathcal {V},\mathcal {E})\)  where nodes \(\mathcal {V}\)  are sentences in \(\mathcal {D}\) , \(\mathcal {E}\)  are undirected edges and are weighted according to matrix \(\mathbf {E}\) , where each element \(\mathbf {E}_{i,j}\)  is the transition probability from vertex \(i\)  to \(j\) .
Similar to Equation REF , \(\mathbf {E}_{i,j}\)  needs to take into account both the inter-sentence similarity and the relevance to \(Q\) , and can be computed as
\(\begin{aligned}&\mathbf {E}_{i,j} = \mu P_r(S_i, Q) + (1 - \mu ) P_r(S_i, S_j) \\&P_r(S_i, Q) \propto \mathrm {sim1}(S_i, Q) \\&P_r(S_i, S_j) \propto \mathrm {sim2}(S_i, S_j).\end{aligned}\) 
